Math AI: Hypothesis Testing (SL Part)

When to use X-squared test for independence?

to see if 2 data sets are independent

what is X-squared test for independence on calculator?

create a matrix, then x² 2-way test

conditions for X-squared test for independence?

• expected value must be over 5

• data must be in a contingency table

null hypothesis for X-squared test for independence?

Ho: variable X is independent of variable Y.

alternative hypothesis for X-squared test for independence?

H1: Variable X is not independent of Variable Y.

purpose of x² goodness of fit test?

if observed value matches expected value

how many lists of data for x² goodness of fit test?

1 data list

Null hypothesis for x² goodness of fit test?

Ho: the data follows uniform distribution
OR
Ho: the data follows normal distribution

alternative hypothesis for x² goodness of fit test?

H1: data does not follow uniform distribution
OR
H1: data does not follow normal distribution

degrees of freedom for x² goodness of fit test?

(number of data points) - 1

degrees of freedom formula in general?

(rows - 1 ) * (coloumns - 1)

purpose of one tailed t test?

when you want to know if a group's average is specifically higher or lower than another

requirements for a t-test?

• sample size is less than or equal to 30

• its assumed to be normally distributed

null hypothesis for one tailed t test?

Ho: mean 1 = mean 2

alternative hypothesis for one tailed t test?

H1: mean 1 > mean 2 (if the question says “greater than,” “increased,” or “more than)
H2: mean 1 < mean 2 (“less than,” “decreased,” or “smaller than”)

how to know which tail is it for one tailed t test?

right tail: if mean is greater than null hypothesis

left tail: if mean is less than null hypothesis

what if P value is GREATER than significant level?

you fail to reject the null hypothesis.

what if P value is LESS than significant level?

you reject the null hypothesis.

what if x² is greater than critical value?

reject null hypothesis

what if x² is less than critical value?

fail to reject the null hypothesis